Generalization of a Result Concerning Projective Planes

Question

Let $\mathcal P$ denote the set of all possible orders of projective planes. For $q\in\mathcal P$, let $PG_2(q)$ denote the projective plane of order $q$. There is a theorem due to James Singler (http://www.ams.org/journals/tran/1938-043-03/S0002-9947-1938-1501951-4/S0002-9947-1938-1501951-4.pdf) that states that if $q$ is a prime power, then the automorphism group of $PG_2(q)$ contains a cyclic subgroup $\langle\sigma\rangle$ which acts regularly on points and acts regularly on lines. I have been told that it has been proven that this result holds for any $q\in\mathcal P$, not just prime powers. Is this true? I suppose no one would be able to disprove this result since doing so would disprove the conjecture that all elements of $\mathcal P$ are prime powers. However, if this has been proven, could someone please provide a reference? Thank you in advance.